Balanced and unbalanced routes to dissipation in an equilibrated Eady flow

Abstract

International audienceThe oceanic general circulation is forced at large scales and is unstable to mesoscale eddies. Large-scale currents and eddy flows are approximately in geostrophic balance. Geostrophic dynamics is characterized by an inverse energy cascade except for dissipation near the boundaries. In this paper, we confront the dilemma of how the general circulation may achieve dynamical equilibrium in the presence of continuous large-scale forcing and the absence of boundary dissipation. We do this with a forced horizontal flow with spatially uniform rotation, vertical stratification and vertical shear in a horizontally periodic domain, i.e. a version of Eady's flow carried to turbulent equilibrium. A direct route to interior dissipation is presented that is essentially non-geostrophic in its dynamics, with significant submesoscale frontogenesis, frontal instability and breakdown, and forward kinetic energy cascade to dissipation. To support this conclusion, a series of simulations is made with both quasigeostrophic and Boussinesq models. The quasigeostrophic model is shown as increasingly inefficient in achieving equilibration through viscous dissipation at increasingly higher numerical resolution (hence Reynolds number), whereas the non-geostrophic Boussinesq model equilibrates with only weak dependence on resolution and Rossby number

Submesoscale Water-Mass Spectra in the Sargasso Sea

“…Primitive equation numerical simulations confirm that strong shears develop on the submesoscale at surface and interior fronts (Klein et al 2008;Capet et al 2008b;Molemaker et al 2010) perhaps accessible with semigeostrophy (Hoskins and Bretherton 1972;Blumen 1978). Moreover, these frontal shears penetrate deeper than predicted by surface quasigeostrophic turbulence theory.…”

“…7), albeit at fixed depths that can include vertical displacements rather than along isopycnals, nevertheless pointing to additional nonquasigeostrophic stirring on the submesoscale being responsible for the observed spectral slopes. Molemaker et al (2010) report that unbalanced motions are important for a submesoscale forward cascade, even though they represent a small fraction of the model domain and energy.…”

“…Tulloch et al's (2011) eddy-resolving numerical simulations revealed that, in weak baroclinic eddy fields without the deep PV gradient reversal that characterizes western boundary currents (i.e., conditions that typify the Sargasso Sea and North Pacific gyres), baroclinic instabilities fill out the submesoscale. Primitive equation simulations of the Eady problem (zero interior potential vorticity gradients) found a nonquasigeostrophic forward cascade associated with frontogenesis, frontal instability, and dissipation in the interior as well as at the surface (Capet et al 2008b;Molemaker et al 2010) and indicated that quasigeostrophic dynamics were fundamentally insufficient to describe the submesoscale even though most of the energy and domain were in quasigeostrophic and hydrostatic balance.…”

“…Passive tracers such as water-mass anomalies on isopycnals are not dynamically constrained by any length scale or balance considerations, and so will eventually cascade to isotropic turbulence and molecular diffusivity scales (Stern 1975;Ferrari and Polzin 2005). While quasigeostrophic (QG) turbulence theory, observations, and numerical modeling have advanced our understanding of subinertial mesoscale physics (Charney 1971;Smith et al 2002;Smith and Ferrari 2009), submesoscale dynamics pose a modeling challenge because quasigeostrophic assumptions break down (Boccaletti et al 2007;Klein et al 2008;Molemaker et al 2010;Capet et al 2008a,b;Tulloch et al 2011) and an observational challenge because internal gravity waves dominate dynamic [horizontal kinetic energy (HKE) and available potential (APE)] signals, leaving only tracers as possible signatures of subinertial submesoscale dynamics. Early attempts to isolate the submesoscale subinertial variability from internal waves observationally using potential vorticity (PV) and other consistency relations were frustrated by demands on time-space sampling (Müller et al 1988;Kunze and Sanford 1993;Kunze 1993;Polzin et al 2003).…”

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

“…In reduced models relevant for geophysical flows, the geostrophic balance that results (between pressure gradients, Coriolis force and gravity) and the quasi-geostrophic (QG) regime, are central tenets of large-scale behavior and have been studied extensively over the years [23][24][25][26], including their breaking down through, for example, fronto-genesis [27].…”